C1 chapter 7 - differentiation

In this chapter we explore how to find the slope or gradient of a curve at each point along it.
We begin to learn a really crucial area of advanced mathematics called calculus.

Sections

C1 section 7.1

To start here you need to be able to:

• evaluate a function at several points including coordinates with decimal values
• find the gradient of a straight line using the techniques taught in C1 chapter 5 -

By the end of this section you will be able to:

• find the gradients of successive chords between increasingly close-by points on a simple curve and spot patterns in the values these give

Examples:

C1 Exercise 7A

• C1 Exercise 7A worked solutions:
  

  C1 Exercise 7A (gradients on curves).jnt
  

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• Questions similar to this exercise:

C1 section 7.2

To start here you need to be able to:

• find the gradient of a straight line using the techniques taught in C1 chapter 5
• manipulate algebra, expanding brackets, collecting terms and cancelling fractions.

By the end of this section you will be able to:

• explain to someone else why the gradient of the graph of y = x² has to be 2x

Examples:

C1 section 7.3

Can you discover the rule to differentiate a polynomial by playing around with this tool that differentiates cubic functions of the form:
$y = a x^3 + b x^2 + cx + d$

C1 Exercise 1A

• C1 Exercise 1A worked solutions: